Problem: Simplify the following expression: $x = \dfrac{-20n^2 + 6n}{-14n^2 + 4n}$ You can assume $n \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-20n^2 + 6n = - (2\cdot2\cdot5 \cdot n \cdot n) + (2\cdot3 \cdot n)$ The denominator can be factored: $-14n^2 + 4n = - (2\cdot7 \cdot n \cdot n) + (2\cdot2 \cdot n)$ The greatest common factor of all the terms is $2n$ Factoring out $2n$ gives us: $x = \dfrac{(2n)(-10n + 3)}{(2n)(-7n + 2)}$ Dividing both the numerator and denominator by $2n$ gives: $x = \dfrac{-10n + 3}{-7n + 2}$